Question: Simplify the following expression: $q = \dfrac{5y^2 - 35y + 50}{y - 2} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ q =\dfrac{5(y^2 - 7y + 10)}{y - 2} $ Then we factor the remaining polynomial: $y^2 {-7}y + {10} $ ${-2} {-5} = {-7}$ ${-2} \times {-5} = {10}$ $ (y {-2}) (y {-5}) $ This gives us a factored expression: $\dfrac{5(y {-2}) (y {-5})}{y - 2}$ We can divide the numerator and denominator by $(y + 2)$ on condition that $y \neq 2$ Therefore $q = 5(y - 5); y \neq 2$